Chinita, I think you need to check the U.S. Citizenship and Immigration Service website at:
http://www.uscis.gov/portal/site/uscis
You may need to get an Immigration Attorney, see:
http://www.uscis.gov/portal/site/us...nnel=648b076eb0f93110VgnVCM1000004718190aRCRD
You also may need a Medical Examination, see:
http://www.uscis.gov/portal/site/us...nnel=95fc9c997f710110VgnVCM1000000ecd190aRCRD
See this website for extending your stay:
http://www.uscis.gov/portal/site/us...nnel=48819c7755cb9010VgnVCM10000045f3d6a1RCRD
You are probably are going to need to file Form I-485, Application to Register Permanent Residence or Adjust Status, and Form I-539, Application to Extend/Change Nonimmigrant Status. Your medical history may only play a small (but possibly important) component of your appeal to stay. I am sorry to say that I believe that your brother passing away will probably not have much bearing on your case.
I would suggest that you check the above websites and gather all your facts. I presume that you are not just asking to extend your stay, but your child's and your husband's, which complicates it. I would further suggest that you draft up the medical section of the above forms, or the letter, if that is what is required, and post here and we will comment on it. You know your background and status far better than we do, and you should be able to write something. We are not your secretaries.
For the most part we do not have background in immigration matters. We do have considerable background in aortic, mitral, etc. valve replacement/repair. But for you to base your appeal simply on the fact that where you would live in Guatemala is not convenient to a medical facility may not carry much weight with the immigration service in your appeal.
Also, bicuspid aortic valves are inheritable. So if your valve problems are due purely to rheumatic fever your offspring should not have valve problems. But if you had a bicuspid valve your offspring may be afflicted.